Towards full molecular gas dynamics simulations of complex flows via the Boltzmann equation

TL;DR

This paper demonstrates the feasibility of directly solving the Boltzmann equation for complex 3D fluid flows using advanced discretization techniques and GPU computing, enabling accurate simulations of phenomena like turbulence and re-entry physics.

Contribution

It introduces a high-performance computational approach combining high-order discretizations and GPU acceleration to solve the Boltzmann equation for complex three-dimensional flows.

Findings

Successful simulation of microchannel flows and turbulence.

Accurate prediction of non-equilibrium effects in re-entry scenarios.

Efficient implementation on massively-parallel GPU architectures.

Abstract

This work explores the capability of simulating complex fluid flows by directly solving the Boltzmann equation. Due to the high-dimensionality of the governing equation, the substantial computational cost of solving the Boltzmann equation has generally limited its application to simpler, two-dimensional flow problems. Utilizing a combination of high-order spatial discretizations and discretely-conservative velocity models along with their highly-efficient implementation on massively-parallel GPU computing architectures, we demonstrate the current ability of directly solving the Boltzmann equation augmented with the BGK collision model for complex, three-dimensional flows. Numerical results are presented for a variety of these problems including rarefied microchannels, transitional and turbulent flows, and high-speed atmospheric re-entry vehicles, showcasing the ability of the approach in accurately predicting complex nonlinear flow phenomena and non-equilibrium effects.